Assuming the noise \(\Gamma _i\)  at each node \(i\)  is following a Gaussian distribution with standard deviation \(\sigma ^P_i\) , then we may apply a Fokker-Planck equation[1]}, [2]}, [3]} to compute the probability distribution of the angular velocity \(\omega \) . It is also a Gaussian distribution with standard deviation
\(\bar{\sigma }^{\omega }=\frac{1}{\sum _{i=1}^{N}M_{i}}\sqrt{\frac{\sum _{i=1}^{N}\left(\sigma _{i}^{P}\right)^{2}}{2\gamma }}.\) 
